Question: $\vec w = (-10,20)$ $\dfrac35\vec w= ($
In general, the scalar multiple of $k$ times $\vec u$ is this: $k\vec u = k(u_x, u_y) = (ku_x, ku_y)$. So, here's how we find $\dfrac35 \vec{w}$ : $\begin{aligned} {\dfrac35}\vec w = {\dfrac35} \cdot (-10,20) &= \left({\dfrac35} \cdot (-10), {\dfrac35} \cdot 20\right) \\\\ &= (-6,12) \end{aligned}$ The answer is $ (-6,12) $.